Operator Ordering in the Relativistic Quantization: Specific Heat in the Rindler Frame
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914012518678528 |
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| author | Sajnok, Karol Dębski, Kacper |
| author_facet | Sajnok, Karol Dębski, Kacper |
| contents | We introduce a covariant canonical quantization for a particle in curved spacetime that tracks operator-ordering ambiguities. Parameterizing spatial and temporal ordering, we derive a Hermitian Hamiltonian with leading quantum-relativistic corrections. In a uniformly accelerated frame, we show the semiclassical heat-capacity approximation misses these effects and then develop a perturbative quantum treatment using Airy-function modes to obtain analytical first- and second-order energy shifts. Including these shifts in the partition function yields nontrivial, ordering-dependent specific-heat corrections. Numerical studies for electrons in extreme electric fields and ultra-light particles in strong gravitational fields demonstrate that these corrections become significant at intermediate temperatures. Enforcing the Tolman-Ehrenfest relation for spatial temperature variation further modulates the heat-capacity profile. Our results suggest that precision calorimetry in laser-acceleration or analogue gravity setups could probe quantum-ordering effects in relativistic regimes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_17362 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Operator Ordering in the Relativistic Quantization: Specific Heat in the Rindler Frame Sajnok, Karol Dębski, Kacper General Relativity and Quantum Cosmology Quantum Physics We introduce a covariant canonical quantization for a particle in curved spacetime that tracks operator-ordering ambiguities. Parameterizing spatial and temporal ordering, we derive a Hermitian Hamiltonian with leading quantum-relativistic corrections. In a uniformly accelerated frame, we show the semiclassical heat-capacity approximation misses these effects and then develop a perturbative quantum treatment using Airy-function modes to obtain analytical first- and second-order energy shifts. Including these shifts in the partition function yields nontrivial, ordering-dependent specific-heat corrections. Numerical studies for electrons in extreme electric fields and ultra-light particles in strong gravitational fields demonstrate that these corrections become significant at intermediate temperatures. Enforcing the Tolman-Ehrenfest relation for spatial temperature variation further modulates the heat-capacity profile. Our results suggest that precision calorimetry in laser-acceleration or analogue gravity setups could probe quantum-ordering effects in relativistic regimes. |
| title | Operator Ordering in the Relativistic Quantization: Specific Heat in the Rindler Frame |
| topic | General Relativity and Quantum Cosmology Quantum Physics |
| url | https://arxiv.org/abs/2506.17362 |